Related papers: Deterministic Chaos vs Integrable Models
We present analytical and numerical results on integrability and transition to chaotic motion for a generalized Ziegler pendulum, a double pendulum subject to an angular elastic potential and a follower force. Several variants of the…
This paper shows that with mechanistic primary budget rules and with some simple assumptions on interest rates the well-known debt dynamics equation transforms into the infamous logistic map. The logistic map has very peculiar and rich…
We review recent progress in analysing wave scattering in systems with both intrinsic chaos and/or disorder and internal losses, when the scattering matrix is no longer unitary. By mapping the problem onto a nonlinear supersymmetric…
We investigate the origin of diffusion in non-chaotic systems. As an example, we consider 1-$d$ map models whose slope is everywhere 1 (therefore the Lyapunov exponent is zero) but with random quenched discontinuities and quasi-periodic…
We describe an example of a $C^\infty$ diffeomorphism on a 7--manifold which has a compact invariant set such that uncountably many of its connected components are pseudocircles. (Any 7--manifold will suffice.) Furthermore, any…
The defining feature of chaos is its hypersensitivity to small perturbations. However, we report a stability of branched flow against large perturbations where the classical trajectories are chaotic, showing that strong perturbations are…
The striking fractal geometry of strange attractors underscores the generative nature of chaos: like probability distributions, chaotic systems can be repeatedly measured to produce arbitrarily-detailed information about the underlying…
Classical chaotic systems are distinguished by their sensitive dependence on initial conditions. The absence of this property in quantum systems has lead to a number of proposals for perturbation-based characterizations of quantum chaos,…
We explore various combinatorial problems mostly borrowed from physics, that share the property of being continuously or discretely integrable, a feature that guarantees the existence of conservation laws that often make the problems…
The large deviations properties of trajectory observables for chaotic non-invertible deterministic maps as studied recently by N. R. Smith, Phys. Rev. E 106, L042202 (2022) and by R. Gutierrez, A. Canella-Ortiz, C. Perez-Espigares,…
The statistics of gaps between quantum energy levels is a hallmark criterion in quantum chaos and quantum integrability studies. The relevant distributions corresponding to exactly integrable vs. fully chaotic systems are universal and…
In many real world chaotic systems, the interest is typically in determining when the system will behave in an extreme manner. Flooding and drought, extreme heatwaves, large earthquakes, and large drops in the stock market are examples of…
The presence of chaos in classical Hamiltonian systems is witnessed by its maximal Lyapunov exponent, that quantifies the instability of motion through the exponential growth of indicators such as the trace of the stability matrix or the…
Quantum chaotic systems are conjectured to display a spectrum whose fine-grained features (gaps and correlations) are well described by Random Matrix Theory (RMT). We propose and develop a complementary version of this conjecture: quantum…
We provide evidence of an extreme form of sensitivity to initial conditions in a family of one-dimensional self-ruling dynamical systems. We prove that some hyperchaotic sequences are closed-form expressions of the orbits of these…
We present an analysis of chaos and regularity in the open Dicke model, when dissipation is due to cavity losses. Due to the infinite Liouville space of this model, we also introduce a criterion to numerically find a complex spectrum which…
Recent progress toward classifying low-dimensional chaos measured from time series data is described. This classification theory assigns a template to the time series once the time series is embedded in three dimensions. The template…
While classical chaos is defined via a system's sensitive dependence on its initial conditions (SDIC), this notion does not directly extend to quantum systems. Instead, recent works have established defining both quantum and classical chaos…
We consider a family of singular maps as an example of a simple model of dynamical systems exhibiting the property of robust chaos on a well defined range of parameters. Critical boundaries separating the region of robust chaos from the…
In classical external gauge fields that fall off less fast than the inverse of the evolution parameter (time) of the system the implementability of a unitary perturbative scattering operator ($S$-matrix) is not guaranteed, although the…